Reasoning about Action: An Argumentation - Theoretic Approach

We present a uniform non-monotonic solution to the problems of reasoning about action on the basis of an argumentation-theoretic approach. Our theory is provably correct relative to a sensible minimisation policy introduced on top of a temporal propositional logic. Sophisticated problem domains can be formalised in our framework. As much attention of researchers in the field has been paid to the traditional and basic problems in reasoning about actions such as the frame, the qualification and the ramification problems, approaches to these problems within our formalisation lie at heart of the expositions presented in this paper

All the shapes of spaces: a census of small 3-manifolds

In this work we present a complete (no misses, no duplicates) census for closed, connected, orientable and prime 3-manifolds induced by plane graphs with a bipartition of its edge set (blinks) up to $k=9$ edges. Blinks form a universal encoding for such manifolds. In fact, each such a manifold is a subtle class of blinks, \cite{lins2013B}. Blinks are in 1-1 correpondence with {\em blackboard framed links}, \cite {kauffman1991knots, kauffman1994tlr} We hope that this census becomes as useful for the study of concrete examples of 3-manifolds as the tables of knots are in the study of knots and links.Comment: 31 pages, 17 figures, 38 references. In this version we introduce some new material concerning composite manifold

Reframing Libel - Taking All Rights Seriously and where it leads us

In preparing this paper, we have returned to first principles and re-evaluated fundamental aspects of libel law, its purposes, its substance, and its processes. Our thinking has been informed by, first, philosophical understandings of democracy and the public sphere and in particular the role of freedom of speech and of the media therein, and secondly, the social psychology of reputation and privacy. By doing this, we are able to ground some of the proposals for reform made previously by Index on Censorship, English PEN, Lord Lester, and others. We do so, however, not through the prism of an over-weaned emphasis on freedom of expression, but rather by triangulating the rights and interests of claimants, defendants, and the wider public. Ultimately, we recommend a coherent set of significant substantive and procedural reforms that if enacted would enhance access to justice and reduce costs for all but the most serious and/or most damaging libels. This involves the recommendation of the introduction of a two-track libel regim

On the works of Euler and his followers on spherical geometry

We review and comment on some works of Euler and his followers on spherical geometry. We start by presenting some memoirs of Euler on spherical trigonometry. We comment on Euler's use of the methods of the calculus of variations in spherical trigonometry. We then survey a series of geometrical resuls, where the stress is on the analogy between the results in spherical geometry and the corresponding results in Euclidean geometry. We elaborate on two such results. The first one, known as Lexell's Theorem (Lexell was a student of Euler), concerns the locus of the vertices of a spherical triangle with a fixed area and a given base. This is the spherical counterpart of a result in Euclid's Elements, but it is much more difficult to prove than its Euclidean analogue. The second result, due to Euler, is the spherical analogue of a generalization of a theorem of Pappus (Proposition 117 of Book VII of the Collection) on the construction of a triangle inscribed in a circle whose sides are contained in three lines that pass through three given points. Both results have many ramifications, involving several mathematicians, and we mention some of these developments. We also comment on three papers of Euler on projections of the sphere on the Euclidean plane that are related with the art of drawing geographical maps.Comment: To appear in Ganita Bharati (Indian Mathematics), the Bulletin of the Indian Society for History of Mathematic

Coherent band pathways between knots and links

We categorise coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterise the minimal coherent band pathways (with intermediates) between any two knots or 2-component links with small crossing number. We demonstrate these band surgeries for knots and links with small crossing number. We apply these results to place lower bounds on the minimum number of recombinant events separating DNA configurations, restrict the recombination pathways and determine chirality and/or orientation of the resulting recombinant DNA molecules